Ultrasonically assisted drilling (UAD) is a non-traditional machining process that employs the vibration of a cutting tool. It offers a better alternative and solution to the challenges of drilling marble using conventional drilling (CD) methods. Machining-induced damage in marble results in the rejection of parts. A significant force reduction is achieved when applying UAD in marble, therefore eliminating large craters created at the exit of the hole in CD, caused by the high force generated. This work presents original experimental results for both drilling techniques, and suggests an analytical model for UAD based on a combination of a contact-problem solution and an incubation-time approach. In the modelling, the problem of fracture at different scales was considered, solved by employing a principle of equal power. The predictions of the presented theoretical model for UAD were validated by comparison with the experimental data, demonstrating a good qualitative agreement.